Presently sounds a little more formal than currently to me but both are formal enough.
Be aware however, that there is understood to be a difference in meaning of this word between American and British English: in the latter it is often used to mean "soon" rather than "right now". With "currently" there is no such confusion.
Note that 'presently' always* means 'currently in Am Eng, but it can mean 'in a little while/shortly' in Br English. Many native speakers of British English use them interchangeably, but some don't. It always meant 'shortly' when my grandfather was around. Some native speakers of Br Eng still hold that 'presently' means 'shortl'y and the way to say 'currently' is 'at present'.
b
PS * I must learn not to pontifocate about other peoples' languages - . I think this is true, at least in describing current usage. (In Br Eng too the 'I'll see to that presently' usage is rather dated.)
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